Coupled resonators have previously been used in optics, and particularly in integrated optics, for the design of various amplitude and phase filtering structures. Previous work on coupled-cavity resonant structures includes: series-coupled-cavity (SCC) structures (FIG. 1), parallel-coupled-cavity (PCC) filters (FIG. 2), and Mach-Zehnder all-pass decomposition (AD) resonant structures (FIG. 3).
Series-coupled-cavity structures (also referred to as coupled-resonator optical waveguides—CROWs—in slow-light literature), such as the structure 310 shown in FIG. 1, may be used as channel add-drop filters and slow-wave structures. The structure 310 includes a chain of linearly coupled optical cavities 311-313, an input waveguide 314 coupled to the first cavity 311, and an output waveguide 315 coupled to the last cavity 313. A drawback of SCC structures is that they only support all-pole spectral responses in the input-to-drop-port response, with no control over the transmission zeros (all located at effectively infinite frequency detuning from the center wavelength). When making a comparison for a given resonant order (i.e., a fixed number of used cavities, or used resonant modes, in the structure), all-pole responses, such as maximally-flat (Butterworth) and equiripple (Chebyshev), are known in circuit theory to be suboptimal in their selectivity in comparison to pole-zero filters, such as elliptic and quasi-elliptic designs. Another drawback is that such all-pole structures are minimum-phase and are, as is well known in signal processing, constrained to have their amplitude and phase response uniquely related by the Kramers-Kronig (Hilbert transform) relation. This means that a flat-top amplitude response implies a dispersive phase response, and high-order, selective (square-passband) filters are as a result highly dispersive. The dispersion can substantially distort an optical signal passing through the filter, so additional dispersion compensating (all-pass filter) structures must ordinarily follow such filters to permit reasonably high spectral efficiency.
With reference to FIG. 2, parallel-coupled-cavity structures 320 have been used as channel filters and for demonstration of light slowing. The structure 320 includes a pair of parallel optical waveguides 321, 322 and a set of optical resonant cavities 323-325. Each of the cavities 323-325 is typically individually coupled to the input waveguide 321 and to the output waveguide 322, while no one of the cavities 323-325 is substantially coupled directly to another cavity 323-325. Parallel-coupled-cavity structures 320 also permit flat-top filter responses in the input-to-drop-port response, i.e., where an input signal enters one waveguide and an output (dropped-wavelength) signal exits from the second waveguide. A drawback of these structures 320 is that there is only one resonator 323-325 at any point separating the input waveguide 321 and output waveguide 322 (in the sense of optical coupling), and higher-order responses may be obtained due to phase-aligned constructive interference of the many cavities 323-325. If substantial variations in the design parameters are introduced due to fabrication errors, the drop port response rejection can be severely reduced, and in the limit of substantial variations may approach a first-order rolloff. A second drawback is that parallel-coupled-cavity structures 320 have interferometric paths between the cavities 323-325 and, as such, their resonant wavelengths are difficult to tune while maintaining the phase relationships of the interferometric paths. The parallel-coupled-cavity structures 320 are also difficult to switch on and off in a hitless manner.
With reference to FIG. 3, a typical Mach-Zehnder all-pass decomposition (AD) structure 330 includes a Mach-Zehnder (MZ) interferometer formed of two waveguides 331, 332 having a first 3 dB coupler 333 and a second 3 dB coupler 334, and resonant cavities 335 in an all-pass configuration in one or the other waveguide 331, 332 inside the interferometer, i.e., between the first and the second 3 dB couplers 333, 334. One advantage of the structure 330 over an SCC filter, such as the filter 310 illustrated in FIG. 1, is that the structure 330 permits optimally sharp, “elliptic” filter response designs. A drawback of these designs, however, is that they require a precise 3 dB coupling (50:50% splitting) in each directional coupler 333, 334, at all wavelengths in the wavelength range of operation. Deviation from 3 dB coupling leads to reduction of the signal rejection ratio in the drop port 336, which appears as a flat “noise floor” because a fraction of light at all wavelengths ventures into the drop port 336. This requirement makes such filters challenging to fabricate and control in practice, as they require an accurate 3 dB coupling over the entire spectrum of operation of the filter (in and out of band).
Referring to FIG. 4, a SCC structure 40 based on standing-wave resonators 41-44 is shown, as known in the prior art. The input port 45 and through port 46 are the incident (incoming) and reflected (outgoing) waves in the top waveguide, respectively, while the drop port 47 is the outgoing wave in the bottom waveguide. An important advantage of microring resonator structures such as the structure 310 depicted in FIG. 1 is that they, by their traveling-wave nature, inherently separate the incoming and outgoing waves into separate waveguide ports. This makes each port automatically “matched” (i.e., matched impedance), each port having no substantial reflection signal when an incident signal is sent into the port. Such structures that inherently have matched ports (as in FIG. 1) can be called “optical hybrids”, and they eliminate the need for optical isolators and circulators.